CBSE Class 12 Mathematics Sample Paper Set M

See below CBSE Class 12 Mathematics Sample Paper Set M with solutions. We have provided CBSE Sample Papers for Class 12 Mathematics as per the latest paper pattern issued by CBSE for the current academic year. All sample papers provided by our Class 12 Mathematics teachers are with answers. You can see the sample paper given below and use them for more practice for Class 12 Mathematics examination.

1. Distance between two parallel planes2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
(a)3/2
(b)5/2
(c)7/2
(d)9/2 

2. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by dP/dx = 100 – 12 √x.
If the firm employees 25 more workers, then the new level of production of items is
(a) 2500
(b) 3000
(c) 3500
(d) 4500

3. Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of A ´ B having 3 or more elements is
(a) 256
(b) 220
(c) 219
(d) 211

4. If the lines

are coplanar, then k can have
(a) any value
(b) exactly one value
(c) exactly two values
(d) exactly three values

5. If the vectors

are the sides of a Δ ABC, then the length of the median through A is
(a) √18
(b) √72
c) 3√3
(d) √45

6. The real number k for which the equation,2x³+3x+k=0  has two distinct real roots in [0, 1]
(a) lies between 1 and 2
(b) lies between 2 and 3
(c) lies between – 1 and 0
(d) does not exist

7.

8. A ray of light along x + √3y = √3 gets reflected upon reaching x-axis, the equation of the reflected ray is
(a) y = x + √3
(b) √3y = x – √3
(c) y = √3x – √3
(d) √3y = x – 1

9. The number of values of k, for which the system of equations (k + 1)x + 8y = 4k kx + (k + 3)y = 3k -1 has no solution, is 
(a) infinite
(b) 1
(c) 2
(d) 3

10. If the equations x x 2 + 2 + 3 = 0 and ax bx c 2 + + = 0,a, b, c ∈ R, have a common root, then a : b :c is
(a) 1 : 2 : 3
(b) 3 : 2 : 1
(c) 1 : 3 : 2
(d) 3 : 1 : 2

11. The circle passing through (1, – 2) and touching the axis of x at (3, 0) also passes through the point
(a) (- 5, 2)
(b) (2, – 5)
(c) (5, – 2)
(d) (- 2, 5)

19. The x-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as (0, 1), (1, 1) and
(1, 0) is
(a) 2 + √2
(b) 2 – √2
(c) 1+ √2
(d) 1- √2

21. The area (in square units) bounded by the curves y = √x, 2y – x + 3 = 0, x-axis and lying in the first quadrant is
(a) 9
(b) 6
(c) 18
(d)27/4

22. Let T_n be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_n + – T_n = 10, then the value of n is
(a) 7
(b) 5
(c) 10
(d) 8

23. If z is a complex number of unit modulus and argument Φ,then arg(1+z/1+z) is equal to
(a) – θ
(b) π/2-θ
(c) θ
(d) π – θ

24. ABCD is a trapezium such that AB andCD are parallel and BC ⊥ CD. If ∠ ADB = θ, BC = p and CD = q, then AB is equal to

25.

(a) 4
(b) 11
(c) 5
(d) 0 

26. The intercepts on x-axis made by tangents to the curve,

(a) ± 1
(b) ± 2
(c) ± 3
(d) ± 4

27. Given A circle, 2x²+2y²=5  and a parabola, y² = 4 √5x .
Statement I An equation of a common tangent to these curves is y = x + √5.
Statement II If the line, y= mx+√5/m(m≠0)  is the common tangent, thenm satisfies m⁴-3m²+2=0.
(a) Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

28. If y = sec (tan^-1 x), then dy/dx at x = 1is equal to
(a)1/√2
(b)1/2
(c) 1
(d) 2

29.

(a) sinA cos A + 1
(b) sec A cosec A + 1
(c) tanA + cot A
(d) sec A + cosec A

30. All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
(a) Mean
(b) Median
(c) Mode
(d) Variance